Publication detail

On Orthogonal Projections for Dimension Reduction and Applications in Augmented Target Loss Functions for Learning Problems

BREGER, A. ORLANDO, J. HARÁR, P. DÖRFLER, M. KLIMSCHA, S. GRECHENIG, C. GERENDAS, B. SCHMIDT-ERFURTH, U. EHLER, M.

Original Title

On Orthogonal Projections for Dimension Reduction and Applications in Augmented Target Loss Functions for Learning Problems

Type

journal article in Web of Science

Language

English

Original Abstract

The use of orthogonal projections on high-dimensional input and target data in learning frameworks is studied. First, we investigate the relations between two standard objectives in dimension reduction, preservation of variance and of pairwise relative distances. Investigations of their asymptotic correlation as well as numerical experiments show that a projection does usually not satisfy both objectives at once. In a standard classification problem we determine projections on the input data that balance the objectives and compare subsequent results. Next, we extend our application of orthogonal projections to deep learning tasks and introduce a general framework of augmented target loss functions. These loss functions integrate additional information via transformations and projections of the target data. In two supervised learning problems, clinical image segmentation and music information classification, the application of our proposed augmented target loss functions increase the accuracy.

Keywords

orthogonal projections; dimension reduction; augmented target loss;

Authors

BREGER, A.; ORLANDO, J.; HARÁR, P.; DÖRFLER, M.; KLIMSCHA, S.; GRECHENIG, C.; GERENDAS, B.; SCHMIDT-ERFURTH, U.; EHLER, M.

Released

23. 8. 2020

Publisher

Springer

ISBN

1573-7683

Periodical

Journal of Mathematical Imaging and Vision

Year of study

62

Number

3

State

Kingdom of the Netherlands

Pages from

376

Pages to

394

Pages count

19

URL

https://link.springer.com/article/10.1007/s10851-019-00902-2

Full text in the Digital Library

http://hdl.handle.net/11012/187007

BibTex

@article{BUT158172,
  author="BREGER, A. and ORLANDO, J. and HARÁR, P. and DÖRFLER, M. and KLIMSCHA, S. and GRECHENIG, C. and GERENDAS, B. and SCHMIDT-ERFURTH, U. and EHLER, M.",
  title="On Orthogonal Projections for Dimension Reduction and Applications in Augmented Target Loss Functions for Learning Problems",
  journal="Journal of Mathematical Imaging and Vision",
  year="2020",
  volume="62",
  number="3",
  pages="376--394",
  doi="10.1007/s10851-019-00902-2",
  issn="1573-7683",
  url="https://link.springer.com/article/10.1007/s10851-019-00902-2"
}